Weak measurement effect on optimal estimation with lower and upper bound on relativistic metrology

Abstract

We address the quantum estimation of parameters encoded into the initial state of two modes of a Dirac field described by relatively accelerated parties. By using the quantum Fisher information (QFI), we investigate how the weak measurements performed before and after the accelerating observer, affect the optimal estimation of information encoded into the weight and phase parameters of the initial state shared between the parties. Studying the QFI, associated with weight parameter $\vartheta$, we find that the acceleration at which the optimal estimation occurs may be controlled by weak measurements. Moreover, it is shown that the post-measurement plays the role of a quantum key for manifestation of the Unruh effect. On the other hand, investigating the phase estimation optimization and assuming that there is no control over the initial state, we show that the weak measurements may be utilized to match the optimal $\vartheta$ to its predetermined value. Moreover, in addition to determination of a lower bound on the QFI with the local quantum uncertainty, we unveil an important upper bound on the precision of phase estimation in our relativistic scenario, given by the maximal steered coherence (MSC). We also obtain a compact expression of the MSC for general X states.

Accepted for publication in Int. J. Mod. Phys. D

References in corpus (20)

• Reference frames, superselection rules, and quantum information
• Entanglement of Dirac fields in non-inertial frames
• Using entanglement against noise in quantum metrology
• Fisher information under decoherence in Bloch representation
• Undoing a weak quantum measurement of a solid-state qubit
• Entanglement-enhanced measurement of a completely unknown phase
• Optimal quantum estimation of the Unruh-Hawking effect
• Continuous variable entanglement sharing in non-inertial frames
• Einstein-Podolsky-Rosen steering and the steering ellipsoid
• Fermionic entanglement that survives a black hole
• Quantum estimation of the Schwarzschild space-time parameters of the Earth
• Processing quantum information with relativistic motion of atoms
• Entanglement generation in relativistic quantum fields
• Quantum-metrology estimation of spacetime parameters of the Earth outperforming classical precision
• Quantum parameter estimation with imperfect reference frames
• Quantum estimation in an expanding spacetime
• Relativistic Quantum Information: developments in Quantum Information in general relativistic scenarios
• Partial measurements and the realization of quantum-mechanical counterfactuals
• Geometric representation of two-qubit entanglement witnesses
• Gravitational parameter estimation in a waveguide

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